{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 4.2 Grad-CAM"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Tensorflow Walkthrough"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 1. Import Dependencies"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import os\n",
    "\n",
    "from tensorflow.examples.tutorials.mnist import input_data\n",
    "from tensorflow.python.ops import nn_ops, gen_nn_ops\n",
    "import matplotlib.pyplot as plt\n",
    "import tensorflow as tf\n",
    "import numpy as np\n",
    "\n",
    "from models.models_4_2 import MNIST_CNN\n",
    "from utils import find_roi\n",
    "\n",
    "%matplotlib inline\n",
    "\n",
    "mnist_cluttered = np.load('./MNIST_cluttered/mnist_sequence1_sample_5distortions5x5.npz')\n",
    "X_train = mnist_cluttered['X_train']\n",
    "y_train = mnist_cluttered['y_train']\n",
    "X_valid = mnist_cluttered['X_valid']\n",
    "y_valid = mnist_cluttered['y_valid']\n",
    "X_test = mnist_cluttered['X_test']\n",
    "y_test = mnist_cluttered['y_test']\n",
    "\n",
    "logdir = './tf_logs/4_2_GCAM/'\n",
    "ckptdir = logdir + 'model'\n",
    "\n",
    "if not os.path.exists(logdir):\n",
    "    os.mkdir(logdir)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 2. Building Graph"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "with tf.name_scope('Classifier'):\n",
    "\n",
    "    # Initialize neural network\n",
    "    DNN = MNIST_CNN('CNN')\n",
    "\n",
    "    # Setup training process\n",
    "    X = tf.placeholder(tf.float32, [None, 1600], name='X')\n",
    "    Y = tf.placeholder(tf.int64, [None], name='Y')\n",
    "    Y_hot = tf.one_hot(Y, 10)\n",
    "\n",
    "    activations, logits = DNN(X)\n",
    "    \n",
    "    tf.add_to_collection('GCAM', X)\n",
    "    tf.add_to_collection('GCAM', logits)\n",
    "    \n",
    "    for activation in activations:\n",
    "        tf.add_to_collection('GCAM', activation)\n",
    "\n",
    "    cost = tf.reduce_mean(tf.nn.softmax_cross_entropy_with_logits(logits=logits, labels=Y_hot))\n",
    "\n",
    "    optimizer = tf.train.AdamOptimizer().minimize(cost, var_list=DNN.vars)\n",
    "\n",
    "    correct_prediction = tf.equal(tf.argmax(logits, 1), Y)\n",
    "    accuracy = tf.reduce_mean(tf.cast(correct_prediction, tf.float32))\n",
    "\n",
    "cost_summary = tf.summary.scalar('Cost', cost)\n",
    "accuray_summary = tf.summary.scalar('Accuracy', accuracy)\n",
    "summary = tf.summary.merge_all()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 3. Training Network"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Epoch: 0001 cost = 1.030643322 accuracy = 0.651499999\n",
      "Epoch: 0002 cost = 0.311122569 accuracy = 0.899800000\n",
      "Epoch: 0003 cost = 0.165329344 accuracy = 0.947400004\n",
      "Epoch: 0004 cost = 0.099200475 accuracy = 0.969800007\n",
      "Epoch: 0005 cost = 0.063634451 accuracy = 0.980600010\n",
      "Epoch: 0006 cost = 0.042079523 accuracy = 0.987400008\n",
      "Epoch: 0007 cost = 0.040920208 accuracy = 0.987100008\n",
      "Epoch: 0008 cost = 0.020570403 accuracy = 0.993800006\n",
      "Epoch: 0009 cost = 0.012259435 accuracy = 0.996100004\n",
      "Epoch: 0010 cost = 0.003470667 accuracy = 0.999200001\n",
      "Epoch: 0011 cost = 0.002051868 accuracy = 0.999800000\n",
      "Epoch: 0012 cost = 0.000328182 accuracy = 1.000000000\n",
      "Epoch: 0013 cost = 0.000159415 accuracy = 1.000000000\n",
      "Epoch: 0014 cost = 0.000116227 accuracy = 1.000000000\n",
      "Epoch: 0015 cost = 0.000092466 accuracy = 1.000000000\n",
      "Epoch: 0016 cost = 0.000076532 accuracy = 1.000000000\n",
      "Epoch: 0017 cost = 0.000064278 accuracy = 1.000000000\n",
      "Epoch: 0018 cost = 0.000054975 accuracy = 1.000000000\n",
      "Epoch: 0019 cost = 0.000047452 accuracy = 1.000000000\n",
      "Epoch: 0020 cost = 0.000041333 accuracy = 1.000000000\n",
      "Accuracy: 0.957\n"
     ]
    }
   ],
   "source": [
    "sess = tf.InteractiveSession()\n",
    "sess.run(tf.global_variables_initializer())\n",
    "\n",
    "saver = tf.train.Saver()\n",
    "file_writer = tf.summary.FileWriter(logdir, tf.get_default_graph())\n",
    "\n",
    "# Hyper parameters\n",
    "training_epochs = 20\n",
    "batch_size = 100\n",
    "\n",
    "for epoch in range(training_epochs):\n",
    "    total_batch = int(np.shape(X_train)[0] / batch_size)\n",
    "    avg_cost = 0\n",
    "    avg_acc = 0\n",
    "    \n",
    "    for i in range(total_batch):\n",
    "        batch_xs, batch_ys = X_train[i * batch_size:(i+1) * batch_size], y_train[i * batch_size:(i+1) * batch_size].reshape([-1])\n",
    "        _, c, a, summary_str = sess.run([optimizer, cost, accuracy, summary], feed_dict={X: batch_xs, Y: batch_ys})\n",
    "        avg_cost += c / total_batch\n",
    "        avg_acc += a / total_batch\n",
    "        \n",
    "        file_writer.add_summary(summary_str, epoch * total_batch + i)\n",
    "\n",
    "    print('Epoch:', '%04d' % (epoch + 1), 'cost =', '{:.9f}'.format(avg_cost), 'accuracy =', '{:.9f}'.format(avg_acc))\n",
    "    \n",
    "    saver.save(sess, ckptdir)\n",
    "\n",
    "print('Accuracy:', sess.run(accuracy, feed_dict={X: X_test, Y: y_test.reshape([-1])}))\n",
    "\n",
    "sess.close()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 4. Restoring Subgraph"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "INFO:tensorflow:Restoring parameters from ./tf_logs/2_7_GCAM/model\n"
     ]
    }
   ],
   "source": [
    "tf.reset_default_graph()\n",
    "\n",
    "sess = tf.InteractiveSession()\n",
    "\n",
    "new_saver = tf.train.import_meta_graph(ckptdir + '.meta')\n",
    "new_saver.restore(sess, tf.train.latest_checkpoint(logdir))\n",
    "\n",
    "activations = tf.get_collection('GCAM')\n",
    "weights = tf.get_collection(tf.GraphKeys.TRAINABLE_VARIABLES, scope='.*kernel.*')\n",
    "\n",
    "X = activations[0]\n",
    "logits = activations[1]\n",
    "activations = activations[2:]\n",
    "\n",
    "sample_imgs = [X_train[y_train.reshape([-1]) == i][5] for i in range(10)]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 5. Generating CAMs"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "last_conv = activations[5]\n",
    "gradients = [tf.gradients(logits[:,i,None], last_conv)[0] for i in range(10)]\n",
    "partial_lin = [tf.nn.avg_pool(gradient, [1, 10, 10, 1], [1, 1, 1, 1], 'VALID') for gradient in gradients]\n",
    "grad_cams = [tf.nn.relu(tf.reduce_sum(last_conv * partial_lin[i], axis=3, keep_dims=True)) for i in range(10)]\n",
    "resized_grad_cams = [tf.image.resize_bilinear(grad_cams[i], [40,40], align_corners=True) for i in range(10)]\n",
    "\n",
    "hmaps = np.reshape([sess.run(resized_grad_cams[i], feed_dict={X: sample_imgs[i][None]}) for i in range(10)], [10, 40, 40])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 6. Displaying Images"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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Z1Ow5UxEREUlb3WoLdVhEEubu6Hu9btuKiIhIuupYW1R77klEtoQjwwBzq36JiIiIVFGl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\nxm+pnGu1AAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1fb1f942a90>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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IgH+1wmVFRESkwMYUW0yUZusSKRAzDv0ZYj+AXSRvJNlAL8F972AHkrsGHv4k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\nDU5ERERERKQQ/j+bkHJxDoNEYAAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1fb4980edd8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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Q9eCkG+WczPi4pZPEMu3ZIDcijFv8WNN+7VnXxeWS9PoFJ5PV2fP+9Cqfa7ph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\nJyIiIiIiUgianIiIiIiISCH8/z7qHpz1QsrsAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1fb4cf79be0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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ERERG0UBii7sAHDKzwwBA8nEA9wI4mPT7GQA/C+B/zTnocCYhayhYkyYL5RbVyy6+lyQ2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\nAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1fb4d09efd0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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4i9hE1y3n2uMeK+5nwbW/ULwAoD4dh231ILndveY6beZd38KXy+njLYhkXkJ9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\nne9EfSwpsKpNUU7sFCbYA3Fl+65b6T4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      "text/plain": [
       "<matplotlib.figure.Figure at 0x1fb7f967b70>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "for i in range(5):\n",
    "    plt.figure(figsize=(15,15))\n",
    "    for j in range(2):\n",
    "        plt.subplot(5, 2, i * 2 + j + 1)\n",
    "        plt.imshow(sample_imgs[i * 2 + j].reshape(40,40), cmap='gray')\n",
    "        plt.imshow(hmaps[i * 2 + j], alpha=0.8)\n",
    "        plt.title('Digit {} Grad-CAM'.format(i * 2 + j))\n",
    "        plt.colorbar()\n",
    "        plt.xticks([])\n",
    "        plt.yticks([])\n",
    "    plt.tight_layout()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.6.2"
  },
  "latex_envs": {
   "LaTeX_envs_menu_present": true,
   "autoclose": false,
   "autocomplete": true,
   "bibliofile": "biblio.bib",
   "cite_by": "apalike",
   "current_citInitial": 1,
   "eqLabelWithNumbers": true,
   "eqNumInitial": 1,
   "hotkeys": {
    "equation": "Ctrl-E",
    "itemize": "Ctrl-I"
   },
   "labels_anchors": false,
   "latex_user_defs": false,
   "report_style_numbering": false,
   "user_envs_cfg": false
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}
